Microstate table

Microstates are the atomic states that result from interactions between electrons in a many electron system (mi and ms values). The microstate table lists all the possible microstates for a given electron configuration arranged according to the Ml and Ms values. In the case of a np2 configuration the microstate table will be of the form... 

In the case of the 3d2 system, the microstate table is as given below, consisting of a total of 45 states. 

Slater determinantal method Part of the microstate table for f2 is given in Table 8.32. 

If we determine all possible microstates and tabulate them according to their and Ms values, we obtain a total of 15 microstates. These microstates can be arranged according to their Mi and Ms values and listed conveniently in a microstate table, as shown in Table 11-2. 

Determine the possible microstates for an configuration and use them to prepare a microstate table. 

Free-ion terms are very important in the interpretation of the spectra of coordination compounds. The following examples show how to determine the values of L, Mi, S, and Ms for a given term and how to prepare microstate tables from them. 

The spin multiplicity is equal to the number of possible values of Mg therefore, the spin multiplicity is simply the number of columns in the microstate table. 

At last, we are in a position to return to the microstate table and reduce it to its constituent atomic states (terms). To do this, it is sufficient to designate each microstate simply by x it is important to tabulate the number of microstates, but it is not necessary to write out each microstate in full. 

To reduce this microstate table into its component free-ion terms, note that each of the terms described in the examples and Exercise 11-2 consists of a rectangular array of microstates. To reduce the microstate table into its terms, all that is necessary is to find the rectangular arrays. This process is illustrated in Table 11-4. Note that for each... 

Reduce the microstate table for the j p configuration to its component free-ion terms, and identify the ground-state term. 

The microstate table (prepared in the example preceding Exercise 11-1) is the sum of the microstate tables for the and terms ... 

For each of the following configurations, construct a microstate table and reduce the table to its constituent free-ion terms. Identify the lowest-energy term for each. 

EXERCISE 11.1 Determine the possible microstates for a S configuration and use them to prepare a microstate table. (Your table should contain 45 microstates )... 

TABLE 11.4 The Microstate Table for and Its Reduction to Free-ion Terms... 

In order to work out the terms for the d configuration, a table of microstates (Table 21.7) must be constructed. However, for interpreting electronic spectra, we need concern ourselves only with the terms of maximum spin multiplicity. This corresponds to a weak field limit. For the d ion, we therefore focus on the E and (triplet) terms. These are summarized in Table 21.9, with the corresponding microstates represented only in terms of electrons with = +. It follows from the rules given in Section 21.6 that the term is expected to be lower in energy than the P term. In an octahedral field, the P term does not split,... 

Determine the number of allowed microstates and sketch a microstate table similar to the one shown earlier for carbon. 

Count the number of microstates that have the same values of Ml and Mj and organize them into a new table similar to the one shown in Figure 4.17. Note that this form of the microstate table will always be symmetric about its center, a fact that can be used to simplify the amount of work involved in the table s construction. 

After removal of the five degenerate microstates that comprise the singlet-D term, the microstate table is reduced as follows (Figure 4.18(b)). 

Microstate table for carbon, with the Ml and M values tabulated across the top and bottom, respectively. 

Determine the term symbols for the N atom. Show all work, (a) Determine the number of possible microstates, (b) Write out all the possible combinations of the electrons in a microstates table, (c) Extract the term symbols and determine the degeneracy of each term, (d) Determine the ground-state term symbol using Hund s rule of maximum multiplicity. 

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